The answer is...it depends
If you live at your domicile, and are lucky enough to get a "3-on, 4-off" schedule, you may be home 22-23 nights in a month. If you live in domicile and bid reserve and "pass" on trips, you may get a couple more nights at home. If you live a long commute from your base, and get some 4-day trips, you may only be home 8 nights. Some of the senior guys I flew with can bid basically all turns (out-and-backs), so they are home every night.
My first month, I commuted cross-country, had a 3-on, 4-off, and was home about 12 or 13 nights. This month, essentially the same schedule, but on reserve, looks like the same 12-13 nights home. Next month, easier commute, but 4-day reserve blocks

so again, probably only 12-13 nights home.
It's really two different jobs, depending on how far you live from where you fly out of...